Quadratic Equations and Functions
Ages 16–18Difficulty adapts to you
Quadratic Equations and Functions
A quadratic has a squared variable. Factorisation is efficient when factors are visible; the quadratic formula works for every quadratic with a ≠ 0. The discriminant b² − 4ac indicates whether there are two, one, or no real roots.
Your goals
- ✓You can solve and interpret quadratics using factorisation, formula, completing the square, and graphs.
- ✓You can use Quadratic Equations and Functions, model correctly.
- ✓You can use the definitions, units, assumptions, and examples to check your answer.
Words to know
- Quadratic Equations and Functions:
- Solve and interpret quadratics using factorisation, formula, completing the square, and graphs.
- model:
- A rule or representation used to describe a situation and make a prediction.
Examples
- 1x² − 5x + 6 = 0 factors as (x − 2)(x − 3), giving x = 2 or 3.
- 2For y = x² − 4, the graph has a minimum at (0, −4) and crosses the x-axis at x = ±2.
Check these
- • Do not skip the meaning of a term or give a result without explaining what it means.
- • Keep every number, symbol, label, and unit in its correct place.
- • Show enough working to check how you reached your answer.
Helpful habits
- • Read the whole question before choosing what to do.
- • Show one clear step at a time and check each step.
- • If you are stuck, draw a model, try smaller numbers, or revisit the example.
Now try your own
Create your own quadratic equations and functions example, solve it, and explain how you checked it.
Spark
Creativity & Innovation“Think outside the box — there is often more than one right answer.”